The present invention is related to a signal processing method and system for reducing noise and enhancing resolution of signal data obtained from; e.g., spectrometer, a digital camera, or a digital sound recorder.
Mass Spectrometry is an analytical technique used to identify compounds based on their molecular weights. There are several basic types of mass spectrometers, all of which rely on similar basic principles. In mass spectrometry, samples are ionized at a source and are selectively accelerated using strong electromagnetic fields to a detector. The result is a discrete frequency distribution of mass to charge ratios detected by the mass spectrometer as a relative (i.e., detector dependent) detector impact intensity. The output is a spectrum of intensity peaks as shown in FIG. 1.
One of the problems that often arise in mass spectrometry (and many other signal processing applications) is the difficulty in distinguishing a real signal from noise produced when obtaining such intensities. Furthermore, any given mass spectrometer has a limited sampling resolution thus causing a single ionized mass to be displayed as a Gaussian distribution rather than a single discrete point. The limited resolution coupled with the noise problem often makes it difficult to identify and separate non-noise signals that are weak and/or so close in proximity to other non-noise signals such that it is difficult to accurately quantify the intensity of peaks that can be used for identifying the compounds. In particular, quantification of weak, noisy and close peaks is very difficult. More generally, low resolution signal data often occurs as a result of hardware limitations. Accordingly, an algorithm that would effectively increase resolution would be very desirable as it is far less costly than improving the hardware.
Accordingly, it would be advantageous to have a signal processing technique that could enhance the discrimination of such non-noise peaks.
The present invention is a method and system for performing a signal processing technique that enhances the discrimination of non-noise wave forms in measurements of a plurality of inputs obtained from a process. In particular, the present invention decomposes or deconvolves a wave form (denoted herein as a composite wave form) obtained from the plurality of inputs into predetermined non-composite wave forms (denoted herein as discrete wave forms, or peaks). More particularly, the present invention can be used to decompose such composite wave forms in signal processing technologies such as mass spectrometry, or any other composite wave form outputting process/application wherein:
(a) the inputs are discrete over a known domain;
(b) the peaks may only occur at predetermined discrete value over the domain;
(c) for each peak of the corresponding measurements for the inputs, there is an expected wave form for which the peak is a maximal value;
(d) the resolution is known by which measurements or readings for inputs to the wave form outputting process/application can be distinguished, i.e., resolution is the finest or smallest discrimination that is available for in measurements or readings from the wave form outputting process/application.
In one embodiment, the present invention can be used for processing mass spectra using linear programming, wherein:
(i) the expected discrete wave forms are Gaussian,
(ii) the predetermined resolution is that of the mass spectrometer being used to obtain intensities for inputs of mass to charge ratios; i.e., the predetermined resolution is the smallest difference in the m/z ratio (more generally, the input values used by the wave form outputting process/application) that the mass spectrometer (more generally, the wave form outputting process/application) can distinguish differences in readings of intensity/amplitude., and
(iii) the resulting peaks can only occur at the discrete points along the mass to charge ratio domain corresponding to atomic mass units. Accordingly, a result from the present invention is a deconvolved spectrum of charge ratios with accurate relative abundances of compounds as one skilled in the art will understand.
When an embodiment of the present invention utilizes linear programming to xe2x80x9cfitxe2x80x9d a sum of Gaussian (discrete wave form) functions to a given (composite wave form) spectrum where each of the discrete wave form functions is approximately centered on some multiple 1 through k of a predetermined value V, then the sum of the composite wave form is given below:                               f          ⁡                      (            x            )                          =                              ∑                          n              =              2                        k                    ⁢                                    c              n                        ⁢                          ⅇ                                                -                                                            (                                              x                        -                        n                                            )                                        2                                                                    a                  2                                                                                        (        1.1        )            
where x is an independent parameter of mass to charge ratios, k is the largest possible center for a discrete wave in the region, cn is the height (or equivalently, intensity or amplitude) of the nth discrete wave form, and a is proportional to the discrete wave form width, and where each discrete wave form is of the form:                               g          ⁡                      (            x            )                          =                  ⅇ                                    -                              x                2                                                    a              2                                                          (        1.2        )            
where a is proportional to the width of the distribution.
In particular, for a given composite wave form to be decomposed, the present invention performs the following steps:
a) Minimizes the vector {overscore (c)}=[c1, c2, c3, . . . , ck] subject to each of the f(xi)xe2x89xa7bi, where bi is the intensity or height of the given spectrum at xi.
b) Maximizes the vector {overscore (c)} subject to each of the f(xi)xe2x89xa6bi, where bi is the intensity or height of the given spectrum at xi.
Note that for mass spectrometry, atomic masses are generally quite close to integral values of one another (i.e., 1 for hydrogen, 2 for helium, etc.). Moreover, it is generally possible to determine the largest ionization charge that can be obtained for a mass spectrometer according to the ionization energy that the mass spectrometer applies to a substance being assayed. In particular, ion charges are typically between +1 and +10. Accordingly, if ions having charges between +1 and +10 are potentially generated, then the predetermined value V mentioned above may be, e.g., a mass-to-charge ratio such as 1/(2*3*5*7)=1/210 of an atomic mass. Note that to simplify the description herein (and without loss of generally), it can be assumed that that the predetermined value V is one, and accordingly the centers of the discrete wave forms are integer values.
To provide additional background material for understanding the present invention, the following references are fully incorporated herein by reference:
1. http://www.asms.org/xe2x80x94The American Society for Mass Spectrometry homepage;
2. Nash, Stephen G., Sofer Ariela, Linear and Nonlinear Programming. McGraw-Hill 1996;
3. Stephen Wolfram The Mathematica(copyright) Book Fourth Edition Wolfram Research 1998; and
4. Applications Guide, Micromass, 1998.
Other features and benefits of the present invention will become evident from the accompanying figures and Detailed Description.